Below are box plots comparing ages at first marriage for a sample of U.S. citizens.

Question

a. What is the median age of first marriage for​ men?
b. What is the median age of first marriage for​ women?
c. Which group has the greater​ range?
d. Compare the first marriage age for men and women.
Age at First Marriage
19
21
23
25
27
Age
WomenMen

Two boxplots showing the age at first marriage for men and women are to the right of a vertical number line that is labeled Age from 19 to 27 in increments of 2. In the left box plot, labeled Women, a box extends from 19.4 to 22 with a horizontal line segment through the box at 20. A vertical line segment extends from the bottom of the box to a horizontal line segment at 19. A vertical line segment extends from the top of the box to a horizontal line segment at 24. In the right box plot, labeled Men, a box extends from 22 to 24.5 with a horizontal line segment through the box at 22.8. A vertical line segment extends from the bottom of the box to a horizontal line segment at 21.3. A vertical line segment extends from the top of the box to a horizontal line segment at 26.
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Question content area right
Part 1
a. The median age for men is
  
23.
​(Round to the nearest integer as​ needed.)
Part 2
b. The median age for women is
  
20.
​(Round to the nearest integer as​ needed.)
Part 3
c. Which group has the greater​ range?
A.
The groups have about the same range.
This is the correct answer.B.
The group of women has a significantly greater range.
Your answer is not correct.C.
The group of men has a significantly greater range.
Part 4
d. Choose the correct comparison below.
A.
Men marry about 3 years later than women. The spread is about the same. About​ 75% of men marry later than​ 75% of women.
B.
Women have a much wider range of ages at which they first marry than men.
C.
Women marry about 3 years later than men. The spread is about the same. About​ 75% of women marry later than​ 75% of men.
D.
Men have a much wider range of ages at which they first marry than women.

Answer 1

Let's go through your questions one by one based on the box plot information you provided.

Part 1

a. The median age for men is:
From the box plot for men, the horizontal line segment inside the box is located at 22.8. Rounding to the nearest integer, the median age for first marriage for men is 23.

Part 2

b. The median age for women is:
From the box plot for women, the horizontal line segment inside the box is located at 20. Rounding to the nearest integer, the median age for first marriage for women is 20.

Part 3

c. Which group has the greater range?
To determine the range, we subtract the minimum value from the maximum value for each group:

• Men's Range: Maximum (26) - Minimum (21.3) = 4.7
• Women's Range: Maximum (24) - Minimum (19) = 5

Comparing the two ranges:

• Men's range: 4.7
• Women's range: 5

So, the group of women has a greater range, leading us to conclude that the correct answer is: B. The group of women has a significantly greater range.

Part 4

d. Choose the correct comparison below.
Looking at the medians:

• Men (23) marry about 3 years later than women (20).

Regarding the spread:

• Women's range is wider than men's.

So the correct choice that encapsulates these comparisons is: A. Men marry about 3 years later than women. The spread is about the same. About​ 75% of men marry later than​ 75% of women.

Note that while you provided many options, A is chosen here because it correctly notes the range being similar although it may have inaccuracies about the spread.

In conclusion:

• a: 23 for men
• b: 20 for women
• c: Women have the greater range.
• d: A is the best option that matches the data provided (but may need to consider the specifics of "spread").